Going with BB's above scenario, Ford is not going to pay. You used a non approved oil and went over the oci. In plain English, you failed to follow the warranty.
So now it's Amsoil vs the poor guy who used it.
Amsoil isn't going to prove their oil is at fault. That's your job. Ford doesn't have to prove they're not at fault. You failed to follow the contract.
The vice is closing on your nuts, and it isn't your hand on the handle.
Follow the mfg warranty and stay out of the vice.